Wentzville School District
Unit 6: Conic Sections
Stage 1 – Desired Results
Unit 6 – Conic Sections
Unit Title: Conic Sections
Course: College Algebra
Brief Summary of Unit: In this unit students will analyze the properties of the conic sections. Students will be able to
graph and write equations in stand form for circles, ellipses, parabolas and hyperbolas.
Textbook Correlation: College Algebra by Barnett, Ziegler, Byleen, Sobecki Chapter 6 (sections 1-3)
Time Frame: 11-13 days
WSD Overarching Essential Question
Students will consider…
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How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
How do I effectively represent quantities and
relationships through mathematical notation?
How accurate do I need to be?
When is estimating the best solution to a
problem?
WSD Overarching Enduring Understandings
Students will understand that…
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Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
strategies.
Concrete understandings in math lead to more
abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
recognize that different natural phenomena can be modeled by circles, parabolas, ellipses, and hyperbolas.
Meaning
Essential Questions
Understandings
Students will consider…
Students will understand that…
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How does the equation tell us which conic section
it represents?
What shapes are formed by the intersection of a
plane and a nappe (two cones sharing an apex)?
What are the important parts of the graphs of
circles, ellipses, parabolas, and hyperbolas?
What are some real-world contexts that can be
modeled with conic sections?
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Acquisition
Graphing a circle and writing its equation in
standard form requires the coordinates of the
center and the radius.
Graphing an ellipse requires the coordinates of
the center, vertices, and co-vertices.
Graphing a parabola requires the coordinates of
the vertex, focus, and endpoints of the focal
chord.
Graphing a hyperbola requires the coordinates of
the center and vertices, and the equations of the
asymptotes
Writing the equation, in standard form, for an
ellipse or a hyperbola requires knowing the
coordinates of the center a (the distance from
center to vertex), b (the distance from center to
co-vertex), and c (distance from center to focus).
Writing the equation, in standard form, for a
parabola requires knowing the value of “p”
(distance from vertex to focus), the coordinates
of the vertex, and the orientation of the parabola
(opening left, right, up, down)
Key Knowledge
Key Skills
Students will know…
Students will be able to….
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conic sections are the figures formed by the
intersection of a plane and a nappe (two cones
sharing an apex)
circles, ellipses, parabolas, and hyperbolas are
conic sections
standard form of the equation of a circle
standard form of the equation of an ellipse
center of an ellipse
major Axis of an ellipse
minor Axis of an ellipse
foci of an ellipse
eccentricity
sum of the focal radii for an ellipse
vertices of an ellipse
co-vertices of an ellipse
standard form of the equation of parabola
focus of a parabola
directrix
axis of symmetry of a parabola
vertex of a parabola
focal chord (latus rectum) of a parabola
standard form of the equation of hyperbolas
focus of a hyperbola
vertices of a hyperbola
transverse axis of a hyperbola
conjugate axis of a hyperbola
center of a hyperbola
asymptotes for a hyperbola
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Graph a circle given its equation in standard form
Graph a circle given its equation in general form
Write the equation, in standard form, for an
ellipse
Graph an ellipse given its equation in standard
form
Graph an ellipse given its equation in general form
Write the equation, in standard form, for a
parabola
Graph a parabola given its equation in standard
form
Graph a parabola given its equation in general
form
Write the equation, in standard form, for a
hyperbola
Graph a hyperbola given its equation in standard
form
Graph a hyperbola given its equation in general
form
Identify a conic section given its equation in
general form
Calculate the eccentricity of a conic section
Standards Alignment
MISSOURI LEARNING STANDARDS
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Show Me-Standards
Goal 1: 1, 4, 5, 6, 7, 8
Goal 2: 2, 3, 7
Goal 3: 1, 2, 3, 4, 5, 6, 7, 8
Goal 4: 1, 4, 5, 6
Mathematics: 1, 4, 5